Abstract
K-means (or called hard c-means, HCM) and fuzzy c-means (FCM) are the most known clustering algorithms. However, the HCM and FCM algorithms work worse for the data set with different shape clusters in noisy environments. For solving these drawbacks in HCM and FCM, Wu and Yang (2002) proposed alternative c-means clustering that extends HCM and FCM into alternative HCM (AHCM) and alternative FCM (AFCM). In this paper, we further extend AHCM and AFCM as Gaussian-kernel c-means clustering, called GK-HCM and GK-FCM. Some numerical and real data sets are used to compare the proposed GK-HCM and GK-FCM with AHCM and AFCM methods. Experimental results and comparisons actually demonstrate these good aspects of the proposed GK-HCM and GK-FCM algorithms with its effectiveness and usefulness in practice.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Bandyopadhyay, S.: An automatic shape independent clustering technique. Pattern Recogn. 37, 33–45 (2004)
Baraldi, A., Blonda, P.: A survey of fuzzy clustering algorithms for pattern recognition Part I and II. IEEE Trans. Syst. Man Cybern. Part B Cybern. 29, 778–801 (1999)
Bezdek, J.C.: Pattern Recognition With Fuzzy Objective Function Algorithms. Plenum, New York (1981)
Blake, C.L., Merz, C.J.: UCI repository of machine learning databases, a huge collection of artificial and real-world data sets (1998). https://archive.ics.uci.edu/ml/datasets.html
Chang, S.T., Lu, K.P., Yang, M.S.: Fuzzy change-point algorithms for regression models. IEEE Trans. Fuzzy Syst. 23, 2343–2357 (2015)
Chen, S.C., Zhang, D.Q.: Robust image segmentation using FCM with spatial constrains based on new kernel-induced distance measure. IEEE Trans. Syst. Man Cybern. -B 34, 1907–1916 (2004)
Dembélé, D., Kastner, P.: Fuzzy c-means method for clustering microarray data. Bioinformatics 19, 973–980 (2003)
Dunn, J.C.: A fuzzy relative of the ISODATA process and its use in detecting compact, well-separated clusters. J. Cybern. 3, 32–57 (1974)
Izakian, H., Pedrycz, W., Jamal, I.: Clustering spatiotemporal data: An augmented fuzzy c-means. IEEE Trans. Fuzzy Syst. 21, 855–868 (2013)
Jain, A.K.: Data clustering: 50 years beyond k-means. Pattern Recogn. Lett. 31, 651–666 (2010)
Kaufman, L., Rousseeuw, P.J.: Finding Groups in Data: An Introduction to Cluster Analysis. Wiley, New York (1990)
Lubischew, A.A.: On the use of discriminant functions in taxonomy. Biometrics 18, 455–477 (1962)
MacQueen, J.: Some methods for classification and analysis of multivariate observations. In: Proceedings of 5th Berkeley Symposium, vol. 1, pp. 281–297 (1967)
Pollard, D.: Quantization and the method of k-means. IEEE Trans. Inf. Theory 28, 199–205 (1982)
Ruspini, E.: A new approach to clustering. Inf. Control 15, 22–32 (1969)
Wu, K.L., Yang, M.S.: Alternative c-means clustering algorithms. Pattern Recogn. 35, 2267–2278 (2002)
Yager, R.R., Filev, D.P.: Approximate clustering via the mountain method. IEEE Trans. Syst. Man Cybern. 24, 1279–1284 (1994)
Yang, M.S.: A survey of fuzzy clustering. Math. Comput. Model. 18, 1–16 (1993)
Yang, M.S., Nataliani, Y.: Robust-learning fuzzy c-means clustering algorithm with unknown number of clusters. Pattern Recogn. 71, 45–59 (2017)
Yang, M.S., Tian, Y.C.: Bias-correction fuzzy clustering algorithms. Inf. Sci. 309, 138–162 (2015)
Yang, M.S., Wu, K.L.: A similarity-based robust clustering method. IEEE Trans. Pattern Anal. Mach. Intell. 26, 434–448 (2004)
Yang, M.S., Wu, K.L.: A modified mountain clustering algorithm. Pattern Anal. Appl. 8, 125–138 (2005)
Zadeh, L.A.: Fuzzy sets. Inf. Control 8, 338–353 (1965)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer Nature Switzerland AG
About this paper
Cite this paper
Yang, MS., Chang-Chien, SJ., Nataliani, Y. (2018). Gaussian-kernel c-means Clustering Algorithms. In: Fagan, D., MartÃn-Vide, C., O'Neill, M., Vega-RodrÃguez, M.A. (eds) Theory and Practice of Natural Computing. TPNC 2018. Lecture Notes in Computer Science(), vol 11324. Springer, Cham. https://doi.org/10.1007/978-3-030-04070-3_10
Download citation
DOI: https://doi.org/10.1007/978-3-030-04070-3_10
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-04069-7
Online ISBN: 978-3-030-04070-3
eBook Packages: Computer ScienceComputer Science (R0)